Analytical prediction of electrowetting-induced jumping motion for droplets on textured hydrophobic substrates: Effects of the wetting states

Electric voltage applied in electrowetting can induce speading, sliding and even jumping of an individual droplet by changing the intrinsic balance of three-phase interfacial tensions, which has been widely used for droplet manipulating in microfluidics and lab-on-a-chip devices in over decades. In the present paper, we present an analytical prediction of jumping velocity for droplets electrowetting on textured hydrophobic surfaces with different wetting states. In particular, we consider a liquid droplet wetting on a textured hydrophobic substrate with a voltage applied between the droplet and the substrate. Once the voltage is turned off, the energy stored in the droplet during the electrowetting releases and could even result in the detachment of the droplet. The effects of the initial and electro-wetting states, i.e. Cassie-Baxter state and Wenzel state, on the jumping velocity of droplets are systematically discussed. Based on energy conservation, the energy conversion between the surface energy, internal viscous dissipation and the kinetic energy of droplets in different wetting states are analysed. The close-form formulas to predict the jumping velocity for different droplet wetting states are systematically derived. Finally, the unified form for predicting the electrowetting-induced jumping velocity of droplets on both flat and textured substrates with different wetting states is obtained, which can describe the jumping motion with various wetting conditions. This work provide theoretical insights on accurate control of the electrowetting-induced jumping motion of droplets on textured hydrophobic surfaces.